In this article, a new nature-inspired optimizer based on bald eagles' fish hunting behavior is proposed for accurate parameters estimation of the solid oxide fuel cells stack's model. The optimal estimated values of the seven control parameters are generated by the bald eagle search (BES) optimizer. These parameters have optimized the model of the solid oxide fuel cells stack and formulated it as an optimization problem with associated constraints. The employed BES optimizer is a flexible algorithm with a relatively large population size which effectively improves the optimization process and has the ability to be improved. The BES optimizer is smooth, rapid, and steady in the convergence process. The BES optimizer is a very simple algorithm that consists of three main stages which are selecting hunting space, searching in the hunting area, and swooping stage. The model of the stack is tested at four operating conditions at 3 bar and varied temperatures of 923/973/1023/1073 K. The BES optimizer leads to more accurate parameters with good convergences. The insignificant values of reported worst mean square errors of something around 4.7e-6 V2 points out the full conformity and coincidence between actual and estimated dataset voltage points. In addition to that, the efficacy of the BES optimizer is assured by comparing the results to parameters estimated from some recent techniques. The cropped estimated polarization curves, V-I and P-I, are very close to the measured datasets at various operating conditions. Statistics metrics indicate the robustness and the viability of the BES compared to other recent challenging optimizers.